The present invention relates to methods and apparatus for interpolating input values of an input signal, whereby output values of an output signal are produced, whose frequency is greater than the frequency of the input signal and whereby the shape of the output signal essentially corresponds to the shape of the input signal.
This kind of interpolation, in which input values occurring at a first frequency are converted into output values occurring at a higher second frequency, is also described as rate changing. This kind of rate changing or interpolation within the meaning of the present invention is used for example in cases where an output signal of a fixed frequency is to be produced without loss of data from time-discrete input signals of varying frequencies. This kind of application results, for example, in the case of data transmission with pulse amplitude modulation. In this case, it is unimportant for the present invention whether the ratio between the frequency of the output signal and the frequency of the input signal is an integer or a non-integer amount.
For interpolation or rate changing, it is known in the prior art to take over the input values and fill them in with certain number of zeros, so that the desired rate or frequency of the output signal is obtained. Apart from this, it is also known to take over the input values and additionally to repeat the single input values, until the desired rate of the output values or the desired frequency of the output signal is obtained. This kind of method is represented in FIG. 2. Here, xn designates a number of input values, to which a higher number of output values is to be assigned. In this case, the output values are designated with zk according to the principle of zero filling and the output values with yk, for the production of which no zeros are used, but input values xn are often repeated. In the cases represented in FIG. 2, the ratio between the frequency of the output signal and the frequency of the input signal is 7, that is to say in each case 7 output values must be produced from one input value.
If the rate change ratio or the ratio between the frequencies of the input signal and the output signal is not an integer amount, particular problems arise. FIG. 3 shows the case where the rate change ratio is 7.5. Both output signals zk and yk are again produced by the method of zero filling described above or holding or repeating single input values. As evident from the diagrams, the output values zk, yk, which are obtained by directly taking over a new input value xn, do not necessarily coincide with these in the time domain. Thus, the second and the third input value xn in each case lie in the time domain between two adjacent output values zk, yk. As a result, the disadvantage arises that the input values xn and the signal changes corresponding to these in the output signal or in the case of the output values zk, yk are not always in phase.
In order to overcome this disadvantage, it is also known to fold the input values xn onto a certain interpolation progression, whereby an interpolation pulse is assigned to each input value xn, which in regard to its time location is aligned to the assigned input value xn. The output values are computed in such a way that they follow the progression of the interpolation pulses. Output values zk, yk produced by this method are represented in FIG. 4, whereby zk replicates the sequence of the output values according to the zero filling method and yk the sequence of the output values according to the holding method. This computation more particularly in the case of the output values yk produced by the holding or repeat method requires an unfavorably high computational cost.